Results 1  10
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11
Optimization Of The Hermitian And SkewHermitian Splitting Iteration For SaddlePoint Problems
, 2003
"... We study the asymptotic rate of convergence of the alternating Hermitian/skewHermitian iteration for solving saddlepoint problems arising in the discretization of elliptic partial differential equations. By a careful analysis of the iterative scheme at the continuous level we determine optimal con ..."
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Cited by 21 (13 self)
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We study the asymptotic rate of convergence of the alternating Hermitian/skewHermitian iteration for solving saddlepoint problems arising in the discretization of elliptic partial differential equations. By a careful analysis of the iterative scheme at the continuous level we determine optimal convergence parameters for the model problem of the Poisson equation written in divgrad form. We show that the optimized convergence rate for small mesh parameter h is asymptotically 1  O(h ). Furthermore we show that when the splitting is used as a preconditioner for a Krylov method, a different optimization leading to two clusters in the spectrum gives an optimal, hindependent, convergence rate. The theoretical analysis is supported by numerical experiments.
BlockTriangular and SkewHermitian Splitting Methods for Positive Definite Linear Systems
 SIAM J. Sci. Comput
, 2003
"... By further generalizing the concept of Hermitian (or normal) and skewHermitian splitting for a nonHermitian and positivedefinite matrix, we introduce a new splitting, called positivedefinite and skewHermitian (PS) splitting, and then establish a class of positivedefinite and skewHermitian s ..."
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Cited by 11 (4 self)
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By further generalizing the concept of Hermitian (or normal) and skewHermitian splitting for a nonHermitian and positivedefinite matrix, we introduce a new splitting, called positivedefinite and skewHermitian (PS) splitting, and then establish a class of positivedefinite and skewHermitian splitting (PSS) methods similar to the Hermitian (or normal) and skewHermitian splitting (HSS or NSS) method for iteratively solving the positive definite systems of linear equations. Theoretical analysis shows that the PSS method converges # Subsidized by The Special Funds For Major State Basic Research Projects G1999032803.
Optimal Parameter in Hermitian and SkewHermitian Splitting Method for Certain Twobytwo Block Matrices
, 2005
"... The optimal parameter of the Hermitian/skewHermitian splitting (HSS) iteration method for a real 2by2 linear system is obtained. The result is used to determine the optimal parameters for linear systems associated with certain 2by2 block matrices, and to estimate the optimal parameters of the H ..."
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Cited by 5 (0 self)
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The optimal parameter of the Hermitian/skewHermitian splitting (HSS) iteration method for a real 2by2 linear system is obtained. The result is used to determine the optimal parameters for linear systems associated with certain 2by2 block matrices, and to estimate the optimal parameters of the HSS iteration method for linear systems with nbyn real coefficient matrices. Numerical examples are given to illustrate the results.
Optimization of the parameterized Uzawa preconditioners for saddle point matrices
 JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, 2009
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PREGULAR SPLITTING ITERATIVE METHODS FOR NONHERMITIAN POSITIVE DEFINITE LINEAR SYSTEMS
, 2009
"... We study the convergence of Pregular splitting iterative methods for nonHermitian positive definite linear systems. Our main result is that Pregular splittings of the form A = M −N, where N = N ∗ , are convergent. Natural examples of splittings satisfying the convergence conditions are construct ..."
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Cited by 2 (1 self)
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We study the convergence of Pregular splitting iterative methods for nonHermitian positive definite linear systems. Our main result is that Pregular splittings of the form A = M −N, where N = N ∗ , are convergent. Natural examples of splittings satisfying the convergence conditions are constructed, and numerical experiments are performed to illustrate the convergence results obtained.
On sinc discretization and banded preconditioning for linear thirdorder ordinary differential equations
 Numer. Linear Algebra Appl
"... Some draining or coating fluidflow problems and problems concerning the flow of thin films of viscous fluid with a free surface can be described by thirdorder ordinary differential equations. In this paper, we solve the boundary value problems of such equations by sinc discretization and prove tha ..."
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Cited by 1 (1 self)
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Some draining or coating fluidflow problems and problems concerning the flow of thin films of viscous fluid with a free surface can be described by thirdorder ordinary differential equations. In this paper, we solve the boundary value problems of such equations by sinc discretization and prove that the discrete solutions converge to the true solutions of the ordinary differential equations exponentially. The discrete solution is determined by a linear system with the coefficient matrix being a combination of Toeplitz and diagonal matrices. The system can be effectively solved by Krylov subspace iteration methods such as GMRES preconditioned by banded matrices. We demonstrate that the eigenvalues of the preconditioned matrix are uniformly bounded within a rectangle on the complex plane independent of the size of the linear system. Numerical examples are given to illustrate the effective performance of our method.
A comparison of iterative methods to solve complex
, 2013
"... valued linear algebraic systems ..."
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WHEN IS THE HERMITIAN/SKEWHERMITIAN PART OF A MATRIX A POTENT MATRIX?
, 2012
"... This paper deals with the Hermitian H(A) and skewHermitian part S(A) of a complex matrix A. We characterize all complex matrices A such that H(A), respectively S(A), is a potent matrix. Two approaches are used: characterizations of idempotent and tripotent Hermitian ..."
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This paper deals with the Hermitian H(A) and skewHermitian part S(A) of a complex matrix A. We characterize all complex matrices A such that H(A), respectively S(A), is a potent matrix. Two approaches are used: characterizations of idempotent and tripotent Hermitian
SemiConvergence Of The Local Hermitian And SkewHermitian Splitting Iteration Methods For Singular Generalized Saddle Point Problems
, 2009
"... In this paper, the local Hermitian and skewHermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving singular generalized saddle point problems were investigated. When A is nonHermitian positive definite and the Hermitian part of A is dominant, the semi ..."
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In this paper, the local Hermitian and skewHermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving singular generalized saddle point problems were investigated. When A is nonHermitian positive definite and the Hermitian part of A is dominant, the semiconvergence conditions are given, which generalize some results of Jiang and Cao for the nonsingular generalized saddle point problems to the singular generalized saddle point problems.